There's no problem in principle to monetising RSS data by sticking ads into the stream. The real problem for Google is (I suspect) that it is a standard protocol, so enables anybody to play, and that means escape from Google's walled garden. In a fit of Apple-envy, and lacking any imagination, Google (and MS) seem to have opted for trying to enforce a walled-garden panopticon as their means to profit, and in that view of the world, RSS -- and, indeed, any other standard protocol -- must die.

RSS isn't easily surveilled. RSS apps download feeds but that doesn't mean an eyeball could have seen any particular item. You could do custom trackable links and charge for clicks, but charging for impressions would be much harder.

Are there other Google ad properties that work that way? (charge only for clicks, not impressions)

Podcasts are largely distributed via RSS, and it’s a blossoming advertising market.

Some services offer to splice audio segments with “current” ads, so that even older content can bring in new ad revenue, if I remember correctly.

You can do ads with RSS, it’s just not as lucrative because the market is small and harder to sell than standard web properties.

I mean if there is an image inside of an item I would assume the RSS reader would optimize for downloading images as needed.

It's not that it "must die", there's just no incentive for Google to keep it around. It's just a cost tagged on to maintenance of Google Groups which can be cost without any major downsides (from Googles perspective).

It's more surprising that they haven't killed Google Groups completely.